If the unit of length is 4 m and that of velocity is `6 ms^(-1)` , the unit of time is (in second)

Options

A. `2//3`
B. `4//3`
C. `3//2`
D. `24`

Answer

To solve the problem, we need to find the unit of time given the unit of length and the unit of velocity.

### Step-by-Step Solution:

1. **Understand the relationship between velocity, distance, and time**:
The formula for velocity (v) is given by:
\[ v = \frac{d}{t} \]
where \( d \) is the distance (or length) and \( t \) is the time.

2. **Identify the given values**:
- The unit of length \( d = 4 \, \text{m} \)
- The unit of velocity \( v = 6 \, \text{m/s} \)

3. **Rearrange the formula to solve for time**:
From the velocity formula, we can rearrange it to find time:
\[ t = \frac{d}{v} \]

4. **Substitute the known values into the equation**:
Now, substitute the values of distance and velocity into the rearranged formula:
\[ t = \frac{4 \, \text{m}}{6 \, \text{m/s}} \]

5. **Simplify the expression**:
When we divide, the meters (m) cancel out:
\[ t = \frac{4}{6} \, \text{s} \]
This simplifies to:
\[ t = \frac{2}{3} \, \text{s} \]

6. **Conclusion**:
The unit of time is \( \frac{2}{3} \) seconds.

### Final Answer:
The unit of time is \( \frac{2}{3} \) seconds.